Dynamic recrystallization is one of the main phenomena responsible for microstructure evolution during hot forming. Consequently, obtaining a better understanding of dynamic recrystallization mechanisms and being able to predict them is crucial. This paper proposes a full-field numerical framework to predict the evolution of subgrain structures upon grain growth, continuous dynamic recrystallization, and post-dynamic recrystallization. To be able to consider a subgrain structure, two strategies are proposed. One relies on a two-step tessellation algorithm to generate a fully substructured microstructure. The second strategy enables for the simulation of the formation of new subgrains during hot deformation. Using these tools, the grain growth of a fully substructured microstructure is modeled. The influence of microstructure topology, subgrain parameters, and some remaining stored energy due to plastic deformation is discussed. The results highlight that the selective growth of a limited number of subgrains is observed only when mobility is a sigmoidal function of disorientation. The recrystallization kinetics predicted with different criteria for discrimination of recrystallized grains are quantitatively compared. Finally, the ability of the framework to model continuous dynamic and post-dynamic recrystallization is assessed upon a case study representative of the hot extrusion of a zircaloy-4 billet (T=650 °C;ε˙=1.0s−1;εf=1.35). The influence of grain boundary properties and nucleation rules are quantified to evaluate the model sensitivity and suitability. Application of these numerical tools to other thermomechanical conditions and microstructures will be presented in an upcoming article.